Nernst effect of Dirac fermions in graphene under a weak magnetic field

The derivation for the transport coefficients of an electron system in the presence of temperature gradient and the electric and magnetic fields are presented. The Nernst conductivity and the transverse thermoelectric power of the Dirac fermions in graphene under charged impurity scatterings and weak magnetic field are calculated on basis of the self-consistent Born approximation. The result is compared with so far the available experimental data.

Figure 1

(Color online) (a) Self-consistent Born approximation for the Current vertex correction. (b) Diagrams for calculating the function $P_{xy}\left({\omega }_1,{\omega }_2\right)$. The vertex $j$ is associated with the vector potential $A_j$. $k^{\pm }=k\pm q/2$.

Figure 2

(Color online) The inverse Hall coefficient $R^{-1}$ (in unit of ${10}^{-3}\text{Tesla}/\text{Ohm}$) as a function of $\delta$. The solid (red) and dashed (blue) lines correspond, respectively, to the calculations with and without the contribution from the last term in Eq. (33) [Inset, the corresponding results for ${\sigma }_{xy}$ normalized by $\sigma B$ with $B$ is in unit of Tesla (T)]. Dot-dashed line: classical result. Symbols: experimental data (Ref. 12).

Figure 3

(Color online) The coefficient $e{N}_{xy}^{12}/T^{2}B$ (red line with circles)(in unit of $\mu V{K}^{-2}{T}^{-1}{e}^2/h$ with $h$ the Planck constant) as a function of $\delta$. The dashed line (green with squares) is $S{\sigma }_{xy}/TB$ for comparison.

Figure 4

(Color online) The coefficient $S_{xy}/TB$ of transverse thermoelectric power (in unit of $\mu V{K}^{-2}{T}^{-1}$) as a function of $\delta$. The solid (red with small symbols) and dashed (green) lines are the calculations at impurity densities $n_i=1.15\times {10}^{-3}{a}^{-2}$ and $1.6\times {10}^{-3}{a}^{-2}$, respectively. The squares (blue at $B=1\text{Tesla}$) and diamonds (cyan at $B=3\text{Tesla}$) are the experimental results of Ref. 2.